Joint Center for Housing Studies
Harvard University
Multiple-Home Ownership and the
Income Elasticity of Housing Demand
Eric S. Belsky, Zhu Xiao Di, and Dan McCue
October 2006
W06-5
The authors would like to thank Greg Ingram, Michael Carliner,
and Yu-Hung Hong for their review and comments.
© by Eric S. Belsky, Zhu Xiao Di, and Dan McCue. All rights reserved. Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that full credit, including © notice is given to the source.
Any opinions expressed are those of the authors and not those of the Joint Center for Housing Studies of Harvard
University or of any of the persons or organizations providing support to the Joint Center for Housing Studies.
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paragraphs, may be quoted without explicit permission provided that full credit, including © notice is given to the source.
Introduction
Traditional models of the income elasticity of demand do not account for the possibility
that households may own two or more homes (Hansen et al. 1998). Although estimates of the
number of second homes and the share of households who own them vary, it is possible to use
existing surveys to narrowly define second homeowners to exclude those who may own
additional properties purely or mostly for investment reasons and then model their housing
choices (Carliner, 2002; U.S. Department of Housing and Urban Development, 2004).
This topic is of interest because it stands to reason that households that divide their
consumption of housing services among two or more properties may make different choices
about their primary residences than households that own a single home. For example, those
splitting their consumption among multiple homes may allocate less, all else equal, to their
primary home and make decisions about the locations of their primary and second homes that
have implications for urban form and the operation of land and housing markets.
This paper examines the determinants of the ownership of multiple homes and the
influence of multiple-homeownership on the income elasticity of housing demand. It explores
the impact of owning multiple homes on the income elasticity of demand for just primary
residences, as well as total housing consumption. To the extent feasible in the datasets used for
this analysis, homes owned for purely investment purposes are excluded from the analysis
because such investments are little different from investments in other non-housing assets.
Homes that are not used by their owners at least in part for seasonal or occasional use do not
produce a flow of housing services that they consume. If the intention is not to use them, there
is little reason to expect ownership of such homes to affect the income elasticity of demand for
primary residences.
Of course owning a home always has an investment element to it because dollars
invested in the home have opportunity costs and homes are typically leveraged investments.
But the twin consumption and investment motives for homeownership are well established and
have not prevented household level estimation of the income elasticity of housing demand.
Both the American Housing Survey (AHS) and the Survey of Consumer Finances
(SCF) are used to model second home demand but only the AHS is used to model the income
elasticity of demand. A logistic regression is used to analyze the determinants of the demand
for multiple-homeownership while log linear models are used to estimate the income elasticity
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1
of demand. We model the impact of the log of estimated permanent income on the log of value
of primary homes for single and multiple home owners separately, after controlling for
demographic characteristics, and with or without a dummy variable for having investment
savings of $20,000 or more. The regression is then repeated to estimate the impact on the log
value for the total of all homes owned by households with more than one home. These models
test for possible differences in the income elasticity of demand for primary residences subject
to the possibility of owning a second home for consumption purposes.
The paper begins with a literature review on the extent and determinants of second
home demand. With few empirical investigations of second homeownership to review, this
part of the review is brief. The literature on estimating the income elasticity of housing demand
is far richer. But much of it focuses on the proper way to measure income for the purposes of
estimating the elasticity of demand, as well as other appropriate controls. Our interest is in the
impact of second homes. Hence, we also indicate how allowing for multiple ownership might
influence elasticities and advance hypotheses about the likely influences on the choice to own a
second home. This section is followed by a discussion of data and methods, model findings,
and conclusions.
Literature Review
Despite the growing market for second homes, there are very few studies of the
determinants of demand for second homes or the propensity of persons to own second homes.
While there are numerous studies on the income elasticity of demand for housing, our review
found no studies that examined the impact of second homes on the income elasticity of demand
either for primary residences or for all residences owned at least in part for consumption
purposes.
Propensities to Own Second Homes
Previous studies of the propensity to own second homes have not used formal
probability models to estimate the independent influence of different variables on the odds of
owning a second home. Using US government data, Di, McArdle & Masnick (2001) explored
the characteristics of the owners of second homes, as well as locations, definitions and
measurements of second homes. The paper found that that second homes are owned primarily
2
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by white, middle aged homeowners with high incomes, and that 40 percent of second homes
are mobile homes, but it did not look at wealth of second homeowners. Looking at wealth,
Gutierrez (1999) searched to find any evidence of a wealth effect on the demand for new
second homes, but concluded that the data were too unreliable to draw definitive conclusions
about whether the wealth building and economic prosperity of the late 1990s were associated
with any increases in second home development in areas with large second home shares.
Kochera (1997) reported rapid growth in recreational properties in the mid 1990’s, but also
large numbers of unexplained “other” second homes not used for recreation or investment
purposes. More recently, Carliner (2002) reviewed data on second homeownership from the
decennial Census, AHS, HVS as well as surveys of homebuyer preferences from NAHB and
NAR, and found that second homeownership is strongly associated with age of homeowners.
He concluded that although the market still appears to be largely misunderstood, studies
indicate that demand for second homes has been holding up and may accelerate somewhat with
increases in income and wealth of homeowners and as more baby boomers enter age cohorts
with traditionally higher second homeownership rates.
In summary, research on the propensity to own a second homes have shown
descriptively that age, race, and income are associated with second homeownership, while
wealth, though not examined on a household level, has been generally assumed to play a role.
No econometric research has been done to study determinants of second home ownership, nor,
as discussed below, have studies been done to measure income elasticity of housing demand in
the context of with and without considering second homes.
Estimating Demand Equations
There is a very rich body of research on the income elasticity of housing demand.
Demand for housing is an embodiment of a consumer’s decision as to how much housing to
consume. Standard theoretical models posit that demand for housing is a function of household
income, the price of housing services, and the price of all other goods and services. The
standard theoretical equation for the housing equation is a log-linear model:
(1) log xi = β0 + β1log y + β2log pH + β3log p0 + u
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In this equation, xi is the annual real expenditure on housing services, y is income, pH is
the relative price of housing, p0 is an index of the price of all other goods, and u is a disturbance
variable. Using a log form, β1 is the true income elasticity and β2 is the true price elasticity of
demand for housing.
The Debate on Current vs. Permanent Income
When it comes to housing demand models, household income is thought of two ways:
current income, which is a highly transitory measurement for earnings in a single year, and
permanent income, which is a long-term concept of what household income will be into the
future. This concept is shown in equation (2), where Yi is current income, YiP is the permanent
income component of current income, and YiT is the transitory income component of current
income.
(2) Yi = YiP + YiT
As a durable good with high transaction costs, it is generally argued that decisions on
housing consumption are based on a household’s permanent income (YiP ), and therefore the
transitory income component of a household’s current income (YiT ) biases demand models that
use current income (Yi ), and results in underestimates of demand elasticities.
A review by Carliner (1973) found that demand models attempting to use measurements
or proxies for permanent income have achieved significantly higher income elasticities than
those using current income. Polinsky and Ellwood, 1979, revisited several studies and showed
that, when substituted for each other within the same housing demand equation, permanent
income elasticities average about 50 percent higher than those for current income. Polinsky and
Ellwood used metropolitan housing sales price and income data to estimate their own measure
of permanent income elasticity and found estimates ranging from 0.80 to 0.87 (Polinsky and
Ellwood, 1979). Since then Goodman & Kawai (1982) have found permanent elasticities to be
100 percent greater than current income elasticities.
Though it is generally agreed that permanent income is the appropriate measurement for
household income within a demand model, there has been much debate over how to correctly
estimate permanent income, and also how to treat current income in the process. Reid (1962)
4
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approximated permanent income by using a restricted sample of households with stable
incomes and using current incomes as a proxy for permanent incomes. Models by Muth
(1965), Winger (1968), and DeLeeuw (1971) used city median incomes as proxies for
permanent income, arguing that averaging incomes across metro areas eliminates transitory
elements. Other studies, such as Carliner (1973) use a multiyear average of a household’s past
four years of incomes to approximate permanent income. More recently, Goodman and Kawai
(1982) define permanent income as the predicted value of a regression of current household
income on the determinant variables of permanent income, with the residual being transitory
income. The resulting equation derived from (2) is as follows:
(3) Yi = φ0 + ΣjφjHj + ΣjφjNj + YiT
where:
(4) YiP = φ0 + ΣjφjHj + ΣjφjNj
In (3) and (4), we see that ΣjφjHj is the sum of a vector of human capital components of
permanent income and their respective coefficients (age, education, employment status), and
ΣjφjNj is a sum of a vector of nonhuman capital components of permanent income. To
determine permanent income, our model follows the methodology of Wachter and Megbolugbe
(1992) in performing a Box-Cox transformation on the dependent variable of the permanent
income regression with λ = 0.5, and then re-transforms the predicted value before including it
in the demand model (see Appendix A for model results).
Incorporating Demographic and Other Household Characteristics
Housing demand models have grown to include a number of demographic variables in
attempts to measure differing “tastes” for housing consumption among a cross section of
households with differing characteristics (Goodman, 1990; Hansen, Formby, & Smith, 1998).
There has been much disagreement as to the significance of demographic factors within
demand models. In a review of several studies, Hansen et. al. (1998) suggests that exclusion of
demographic variables likely to be correlated with permanent income, such as race, age, sex,
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5
and household size, will bias estimations of income elasticity, and that the direction of this bias
is most likely upward. However, an earlier empirical study by Carliner (1973) finds income
elasticity measurements from regressions using demographic terms are higher than those
without. Another empirical study from Follain (1979) found income and price elasticities not
sensitive to the presence of socio-demographic variables, and a third empirical study by
Goodman (1990), found demographic interactions relatively insignificant for populations close
to general population means but highly significant for populations away from means, such as
those at very low or very high incomes. In light of this diverse array of findings, we felt it
necessary to include demographic variables within our model, and that age, race, and family
type were the most appropriate factors available within our dataset.
Controlling for House-Price and Non-Housing Cost Indexes
The standard demand model in equation (1) generates price and income elasticities of
housing demand based on the utility of housing consumption relative to all other goods.
Goodman & Kawai (1984), following examples from DeLeeuw (1971) and Polinsky and
Ellwood (1979), estimate a demand model with demographic and housing characteristic
variables but without a non-housing cost index, choosing instead to apply various fixed-effect
coefficients within the Ordinary Linear Regression.
Due to limited geographic data in the AHS dataset, our model uses this fixed-effect
approach to control for relative differences in both house-price and non-housing costs based on
regional location as well as metro / non-metro area location.
Our fixed-effect estimated regression equation becomes:
(5) log (hi ) = β0+ β1log yiP + ΣjφjZji + u
Where hi is the value of housing consumption and Zji is a vector of our 12 geographic
dummies to control for the relative price of housing and non-housing goods to the individual,
as well as demographic and other housing characteristic dummy variables that potentially affect
the demand for housing and control for fixed-effects on housing consumption within the model.
6
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We use housing value as our measure of housing consumption (hi) in our equation.
Researchers generally agree that housing consumption for homeowners is best approximated
and more easily obtained as a standardized measurement of total housing value, rather than as
annual expenditures on homeownership. The common method, used by Goodman and Kawai
(1984), involves hedonic regression, whereby a household’s housing value is taken as a
function of neighborhood and resident characteristics. The housing price index can be
determined by the price of a standardized unit of housing according to the hedonic regression,
and housing consumption can then be measured as housing value divided by the price of a
standardized unit. Including geographic and socioeconomic characteristics within our fixedeffects model enables us to standardize housing value somewhat within the demand model;
though using separate hedonic regressions would clearly be superior. Therefore, hi, in our
model is approximated simply as the total value of housing.
Controlling for Other Effects: Wealth and Elderly Status
Wealth variables seem not to have been included in previous studies, although it may
have an impact on the propensity of second home ownership and influence on income elasticity
estimates. Also, although age has often been included in studies of income elasticity, its effect
may not be linear and its interaction with income is very possible. The lack of these variables in
previous studies encourages us to include them in our study.
Measures and Magnitude of Second Home Demand
This paper is not intended to reopen debates about the level of income elasticity of
housing demand. Instead, it explores whether ownership of second homes influences the
income elasticity of demand for primary residences or for the aggregate value of all homes that
are owned, at least in part, for consumption. This is increasingly relevant given the apparent
increase in second homeownership in recent years.
Statistics on the extent of second homeownership and the number of second homes are
often inconsistent. These inconsistencies mostly reflect differences in methods of data
collection, especially in how questions about the purpose of vacant or additional owned
properties are asked, but also as a result of differences in sample sizes, sampling procedures,
and weighting procedures across surveys.
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7
The AHS, Housing Vacancy Survey (HVS), and decennial Census each contain
estimates of the number of second homes based on interviewer efforts to determine the status of
vacant units. The AHS and the HVS produce estimates of second homes (defined here as
homes for seasonal or occasional use and homes occupied by those with a usual residence
elsewhere) that are closer to each other than to the decennial Census, which consistently
estimates a far smaller number of second homes. However, the AHS produced higher second
home estimates than the HVS in the early to mid 1990s and then lower estimates thereafter
(Carliner 2002). The HVS registered a strong 20 percent increase in the number of second
homes from 1995 to 6.8 million in 2005 while the American Housing Survey reported a smaller
but still substantial increase from 5.8 million in 1995 to 6.2 million in 2003.
Many surveys ask households questions about whether they own additional properties
and then ask them questions about these properties. These include the AHS, the SCF, the
Survey of Income and Program Participation (SIPP), the Panel Study of Income Dynamics
(PSID), and industry surveys such as one of new homebuyers conducted by the National
Association of Home Builders (2000) and by the National Association of Realtors® (NAR) of
homebuyers and homeowners. A recent NAR survey of 2005 homebuyers found that about 12
percent of all homes purchased were characterized by their owners as for vacation use and 28
percent for investment purposes. The intricacies of how all the other household surveys are
conducted are well summarized by Carliner (2002) and the US Department of Housing and
Urban Development (2004). Suffice it to say here that the SCF is the only dataset to ask
questions about second homes on a regular (every three year) basis. Like the HVS, it shows
growth in second home demand over the past decade (Chart 1). However, for all age groups
except those now in their 60s, all of the growth was in households reporting timeshare
fractional ownership in a second home. Overall, the SCF shows an increase of about 600,000
homes for “seasonal/vacation use” and in time shares of fully 1.8 million. Assuming that
fractional ownership averages 2 week per year, then a 1.8 million increase in timeshare owners
translates into only about 70,000 units.
8
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Share of households
having timeshares
14%
12%
10%
8%
6%
4%
2%
0%
30s
40s
50s
60s
2004
1995
2004
1995
2004
1995
2004
1995
2004
Age
Share of households
having
seasonal/vacation
homes
1995
Share of
Households
Chart 1: Second Home Ownership Has Increased
Across All Ages
70+
Source: SCF data
While the figures shown here suggest that second homeownership rates among
homeowners peak in their 50s and 60s at about 6-6½ percent, and rates of time shares peak at
about 5 percent, these may be undercounts. The reason is that when SCF respondents are asked
what type of property they own, they must choose from “seasonal/vacation home,” “time share
ownership,” and a host of structure types including single-family house, condominium,
residential, trailer/mobile home, farm/ranch, etc. It is likely that some of those who own homes
for occasional use on weekends or for work do not consider them for seasonal or vacation use.
Indeed, many of those responding with a structure type do not derive any rental income from
their second home, suggesting that in some cases they are at least in part for consumption uses.
With an even greater number of households headed by younger boomers growing into
the 50-59 age group by 2015 than the number of households headed by leading edge boomers
currently in that age, and each generation accumulating more household net wealth and higher
median incomes than previous generation at similar age, demand for second homes are likely to
continue to grow in the coming decade (Belsky and Prakken 2004).
Hypotheses
The literature and economic theory suggest the following hypotheses with respect to the
likelihood of owning a second home and the impact of owning a second home on income
elasticities for housing:
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A) The likelihood of owning a second home will be increasing with permanent income,
current income, wealth, and age. Higher incomes and wealth allow consumers to
allocate more of the household budget to housing consumption and investment.
Lifecycle factors suggest that even after controlling for income and wealth, second
homeownership might be higher for older aged households as they approach or reach
retirement and look towards more leisure time. But the impact of the presence of
children is more ambiguous because on the one hand it may increase the utility derived
from a second home, but on the other may be a drain on the household budget.
Geographic location of the primary residence might also have an influence, but again is
ambiguous. With most owners having second homes within driving distance of their
primary residences, living in a lower cost area could increase the likelihood of owning a
second home because the costs of buying a second home are lower. On the other hand,
these same areas tend to have lower price appreciation and therefore leave owners with
less housing wealth to leverage up for second homeownership.
B) The income elasticity of demand for primary residences will be lower for those with
second homes than for those with just one home. There are several factors that lead to
this expectation. First, households that have a preference for owning second homes
divide their housing consumption among more than one property. Because they split
their consumption between two homes, one would expect the income elasticity of
demand for just their primary home to be lower than for owners of only one home. This
holds true whether the initial decision on how much to spend on a primary residence
was made with the intention of buying a second home or if instead, over the lifecycle, a
homeowner decides to adjust their housing consumption upward by investing in a
second home rather than trading-up to a higher valued home or improving their primary
residence. Second, second home owners have higher average incomes and housing
consumption levels relative to owners of just one home. Indeed, their average income is
very close to that of owners in the upper income quartiles of a just a single residence.
Therefore, second home owners may be closer to being fully housed. In this case, uses
of an incremental dollar other than housing may maximize their overall utility. As a
result, increases in income may not in turn result in as large a percentage change in
10
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consumption in their primary (or secondary) homes. Lastly, owners of a single home
with no desire for second homeownership may have more of an incentive to maximize
the quality and consumption value of their sole home, while those with a propensity to
own second homes may under-consume their primary house in favor of second home
ownership.
C) The income elasticity of demand with respect to all houses owned by second
homeowners will be lower than the elasticity of just their primary property. With
consumption split, spending on the primary home will take precedence over spending
on the secondary home, and therefore lower elasticities of secondary home demand will
drag down overall elasticities of demand which incorporate both primary and secondary
home consumption. Given the same income distribution, the income elasticity of
demand for the primary home (eP) relates to the elasticity of the second home (eS) as a
ratio based on the way in which consumption of these two goods relate to each other,
based on the formula 1 :
(6) eS = eP (% Change S / % Change P)
With this equation, if both primary and secondary consumption are treated equally, the
two income elasticities are equal. But we posit that consumption of primary home is the
first priority because that is where homeowners spend more of their time. Therefore an
incremental dollar will contribute more to consumption of a primary home than a
second home. Thus, eS is less than eP. So it follows that the elasticity of total housing
consumption should be higher than the elasticity for the second home, but lower than
for primary home consumption. This should be at least true for non-elderly but seniors
may spend half or even more time in their second homes.
1
With income Y, the primary elasticity is : eP = (dP/P) / (dY/Y) and the second is eS = (dS/S) / (dY/Y);
Solving for y in the former equation, we obtain Y = (eP*P*dY)/dP and substituting this into the latter equation, we
have:
eS = eP * (dS/S)/(dP/P), which can be re-written as: eS = eP * [(% Change S) / (% Change P)].
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11
D) The income elasticity of demand with respect to all properties owned by those who have
second homes for consumption purposes will be lower than that of single-home owners.
This is because, similar to the reasoning in (B) above, second homeowners, being on
average older with high levels of wealth and income and high levels of housing
consumption already, are less likely to be under-housed than the generally lower
income owners of a single home. Therefore, income increases are not matched by the
same increases in housing consumption seen by the generally lower income owners of a
single home only. This may be tested and seen through decreasing elasticities of
demand among single-home owners as income levels increase.
E) Models that do not include the value of second homes and do not control for second
homeownership are likely to produce biased estimates of the income elasticity of
housing demand. This is because the ownership of multiple homes is expected to
influence the income elasticities of demand in the ways stipulated in (A)-(D) above.
Data and Method
We use the AHS and SCF to provide empirical evidence on determinants of secondhome ownership and AHS to explore income elasticity of housing demand when second
homeownership is considered. The AHS is conducted by Census for HUD every two years at
the national level, and only twice (in 1985 and 1995) did it have a supplemental survey on
second homes. In these years, respondents were asked about other residential properties they
owned in addition to their primary homes. For these properties, up to 6 such properties are
surveyed. For each recorded property, it asks respondents about why they hold such a property
and asks them to mark all the reasons that apply. In our paper, we only look at those properties
that are marked for recreational use in order to narrow the field as much as possible to
households that self-report homes that they view, at least in part, as providing them a flow of
housing consumption services.
The regular AHS survey contains detailed household information including current
household income, age, race/ethnic background, the education level of household heads, and
family type. Unfortunately, geographic detail in the dataset is lacking. While about 100
metropolitan areas are specified, in most cases the number of observations is far too few to
12
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create a meaningful hedonic price index. Instead, to control for differences in the costs of
housing and non-housing goods across areas, we rely on the interaction of the 4 census regions
and 3 types of metropolitan status (cities, suburbs, or non-metro). This provides 12
variations—an admittedly crude control for housing price differences across the country.
The AHS also has a dummy variable on whether the household has investment savings
of $20,000 or more. This is a crude proxy for the level of non-housing wealth of a household.
This could have an impact on the income elasticity of housing demand but the current literature
overlooks potential wealth effects on income elasticity. Particularly for the propensity of
second-home ownership, it may have some influence as a determinant.
Exhibit 1 shows basic descriptive statistics on the variables from the AHS we use to
model propensities and elasticities. Because AHS top-codes the value of primary homes at
$375,000, we drop these roughly 3 percent of cases in all of our elasticity models to avoid
using exactly the same value for all records with house values at the top code. Importantly, the
second home value is not top-coded, so models of the total value of properties owned by people
who own a home under $375,000 in 1995 are not right-censored on second-home value. We
also exclude a couple of hundred cases (less than one percent of the entire sample) in our
elasticity models involving owners of multiple homes where no information on the value of
second homes was provided.
The SCF is conducted by the Federal Reserve Bank every three years. The most recent
survey is 2004 and was just released in March 2006. The survey was originally designed to
measure all kinds of debt that people take on, and thus has very rich information on liabilities
vs. assets and therefore the net wealth held by each household surveyed. Because of the
imbalances in wealth holding and distribution, the SCF over samples wealthy households.
Roughly half of its sample is a set of wealthy households and the other half are households
distributed across a greater spectrum of household wealth. Because of that, we have to use a
weighted sample in modeling work.
One of the benefits of this sampling procedure is that it insures better accuracy at the
level of aggregate household net wealth. Therefore, one of the advantages of using the SCF
data to model the probability of owning a second home is that SCF data provide the most
accurate and detailed wealth information of any household survey. With this data, we are able
to obtain non-housing wealth as a variable that omits home equity, which is too closely
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13
correlated to our dependant variable of home value and would induce bias our model. This is
more precise than the AHS dummy indicator of savings in excess of $20,000.
The biggest limitation of the SCF data is that it has a small sample size of less than
5,000 households. Because of that, the released file for public use does not have any geographic
variables. This prevents us from controlling for any house price variation across even regions
or metropolitan status. It also prevents meaningful estimation of permanent income. For this
reason, we only use SCF data to model the propensity of owning a second home. The SCF also
has some intrinsic problems embedded in the questionnaire design. As noted above, the coding
system is such that some households may have chosen structure type categories such as singlefamily or multi-family units even though the home they own is for their own seasonal or
occasional use. Exhibit 2 displays some descriptive statistics of homeowners in the SCF data.
Because we run models on weighted samples, both un-weighted and weighted statistics are
displayed.
The two different datasets have different estimates on the share of vacation home
owners among all households. While 2004 SCF data indicate a 3.7 percent vacation
homeownership rate, the 1995 AHS data show a 3.3 percent rate. That is not surprising when
considering the growth of vacation homes during the decade and differences in how questions
about the purpose of second properties are asked. In both data, we exclude timeshare units from
our count of recreational second homes.
With the compelling theoretical and empirical arguments for using permanent income
rather than current income as the appropriate correlate to estimate income elasticity, in our
preferred AHS models we use the Box-Cox square root transformation in a two-step method
first estimating household permanent income as described in Appendix A and then plugging in
predicted values into the propensity and income elasticity of demand regressions. We did not
estimate permanent income in SCF data because it lacks any kind of geographic information
control for regional wage differentials. Thus, in our models using AHS data we put in
permanent income while in our propensity model using SCF data we put in both current
household income and the education level of household heads, which is often a proxy indicator
for permanent income.
In our elasticity models, we run non-elderly (Table 4a) and elderly (Table 4b) samples
separately, as we suspect they may have statistically significant differences in elasticity with
14
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may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
respect to permanent income, especially since our predicted values for permanent income are
apt to have larger residual errors for older people because the correlation of current incomes
and the right-hand side predictors is weaker for retirees. We also run models with (Tables
4a/4b) and without (Tables 4c/4d) the wealth variable to see how it affects other coefficients,
especially income elasticities.
In Model 1, we estimate the elasticity among those who own only a single home, using
the value of primary home as the dependent variable. In Model 2, we estimate the elasticity of
demand for just the primary residence among those who own more than one home, again using
the value of primary home as the dependent variable. This is our principal test of the hypothesis
that the income elasticity of demand for primary residences will be lower for second
homeowners than others because they split their consumption among multiple properties.
In Model 3, we estimate the income elasticity of demand using total value of all homes
owned by owners with second homes as the dependent variable to test the hypothesis that it will
be lower because a percentage point increase in income will bring about a smaller percentage
point increase in a larger combined first and second home total value. In Model 4, we estimate
the income elasticity of demand just for second homes among second homeowners to test the
hypothesis that it will be lower than the primary home demand elasticities, indicating relatively
low income elasticities for second home demand, preference for primary home consumption,
and most importantly, the negative influence of second home ownership on demand elasticities
for total housing consumption. In Model 5, we present a single model of housing value for all
homeowners with a dummy variable indicating ownership of a second home. This is included
to provide an unbiased estimate of the income elasticity of housing demand that incorporates
the possibility of second home ownership.
Lastly, we perform a secondary test of the hypothesis that, because they have higher
average incomes than the general population of homeowners that own just one home, second
home owners have lower elasticities of demand for primary residences. To accomplish this, we
divide the owners of one home into income quartiles to see if the income elasticity of demand
is in fact lower among owners with average incomes similar to the population of second home
owners.
It should be noted that our data do not include geographic controls for second home
location. Therefore, since our models proxy housing consumption with house value,
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
15
uncontrolled-for location-based differences in appreciation levels of second homes may bias
measurements of income elasticities based on current second home values. Although most
second homes are within driving distance of the first home and may have similar rates of
appreciation, if a significant number of second homes bought at the same price point had
significantly different appreciation rates, then the current value does not equally reflect total
home consumption. In the end, we assume that second home location and appreciation rates
have some effect on income elasticities and owners’ adjustments to housing consumption that
lie beyond the scope of this paper.
The functional form of our propensities models is logistic and the form of our elasticity
models is log-linear. Hence the variables in propensities infer differences in the odds of
owning a home conditional on each individual variable holding the others constant. The
coefficients on income in the log-linear models can be interpreted as the elasticity of housing
demand with respect to income and assumes constant elasticities across all values of the
dependent variables.
More formally, our logit model takes the following form:
(7) P(Si ) = φ0 + φ1YiP + φ2MINORITYi + ΣψjAGEji + ΣτkFAMILYki + ΣωlGEOGRAPHYli
+ φ3ELDERINCOMEi + Ui
Where P(Si ) is the probability of owning a second home, YiP is permanent income,
MINORITY is a dummy variable indicating whether or not the household head is non-Hispanic
white (1 if minority and 0 otherwise); AGEj is 4 dummy variables flagging 10-year age cohorts
(35-44 years, 45-54 years, 55-64 years, and 65+ years old, with under 35 as the reference
group); FAMILYk is 5 dummy variables flagging the type of family (married with children,
single parents, other family type, single person, and other non-family type, with married
without children as the reference group); GEOGRAPHYl is 11 dummy variables controlling for
regional and metropolitan level fixed effects (Northeast suburb, Northeast non-metro, Midwest
city, Midwest suburb, Midwest non-metro, South city, South suburb, South non-metro, West
city, West suburb, West non-metro, with Northeast city as the reference group), and Ui is a
disturbance variable. In our propensity model using AHS data we also include an interaction
16
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may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
variable ELDERINCOME containing the income of elderly assuming their income may have
quite different impact on second home ownership.
Our elasticity models take the following form:
(8) log (hi ) = β0+ β1log yiP + β2SAVINGSOVER20K + β3MINORITYi + ΣτkFAMILYki +
ΣωlGEOGRAPHYli + Ui
Where hi is the value of the primary home or the total value of all homes; yiP is the
predicted permanent income; wi is a dummy variable flagging household savings and
investments of over $20k (1 if yes and 0 otherwise); MINORITY is a dummy variable
indicating whether or not the household head is not non-Hispanic white; FAMILYk is 5 dummy
variables flagging the type of family (married with children, single parents, other family type,
single person, and other non-family type); GEOGRAPHYl is 11 dummy variables controlling
for regional and metropolitan level fixed effects (Northeast suburb, Northeast non-metro,
Midwest city, Midwest suburb, Midwest non-metro, South city, South suburb, South nonmetro, West city, West suburb, and West non-metro); and Ui is a disturbance variable.
Findings from the Propensity Models
Models run on both the AHS and SCF data find that age is the most predominant
determinant for vacation homes. The AHS model finds that the odds of owning a vacation
home are 3.7 times higher for 45-54 year olds than the odds for those under 35. For the age
group between 55 and 64, the odds ratio is as high as 6.5. In our SCF model, the numbers are
even more dramatic. Compared to the odds for household heads under 35, the odds of owning a
vacation home are 11.2 times as large for those between 55 and 64 years old. Why this should
be true even after controlling separately for income and especially wealth (which we can do
with some precision in the SCF model) is unclear. Wealth is correlated with age so it is
conceivable that the estimates on age are biased and picking up some of the wealth effect. It
could also be that at later ages, mortgage payments of homeowners make up a smaller share of
their overall budget, freeing them up to spend more on a second home. Nevertheless, it seems
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
17
plain that lifecycle matters a great deal when it come to the likelihood of owning a second
home.
Both datasets suggest that minority households are less likely to own second homes, all
else equal. Both income (current and permanent) and non-housing wealth are positively
associated with second homes in both datasets. But in our propensity model using SCF data,
though these two variables are statistically significant, they have little practical impact. With
$10,000 more non-housing wealth, a household’s odds ratio of having a vacation home vs. not
having one is only 1.001, and a $10,000 increase in household current income only raises the
ratio to 1.005. Again, this is surprising and suggests that the correlation of age with wealth and
income may be distorting the results.
In the SCF data, education is positively associated with owning a second home. The
estimated odds that a college educated household head would own a vacation home versus no
vacation home are over 4 times more than that of a household head with less than high school
education. In AHS data, there is statistically significant interaction between permanent income
and elderly status, suggesting that the impact of permanent income on propensity is indeed
different for elderly and non-elderly households.
None of the geographic dummy variables in AHS is statistically helpful in predicting
second homes. So second-home ownership is not favored or disfavored by homeowners in any
particular location regarding their primary residence. Having investment savings of more than
$20,000 in the AHS data or higher level of non-housing wealth in the SCF data is more likely
to own a vacation home. Exhibit 3a and 3b show our propensity models in AHS and SCF data.
The patterns observed in two different data sets collected 9 years apart seem amazingly
consistent.
Findings from the Elasticity Models
We obtain log-linear estimates in our elasticity models. Both among the non-elderly and
elderly households, our models show that vacation home owners have somewhat lower income
elasticity of demand for primary housing (Model 2) compared to those not having vacation
homes (Model 1). When adding the value of vacation homes to that of primary homes, the
elasticity is further lower (Model 3) compared to those without second homes, having been
dragged down by very low demand elasticities for second homes (Model 4). For comparison to
18
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may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
the above, our estimate of the normal income elasticity of demand for all housing consumption
among all homeowners (Model 5) shows that there is a slight positive bias in models that fail to
incorporate the lower fixed effects behind second homeownership. These results are in line
with our expectations.
In our models, income elasticity estimates among the non-elderly sample are higher
than those found among the elderly sample, though in part this reflects larger sample sizes for
the non-elderly. Taking out the dummy variable on investment savings of $20,000 or more does
not change the elasticity pattern (see Exhibit 4c-4d in comparison to 4a-4b).
Our additional test of income elasticities by income level for those not owning a
vacation home (Exhibit 5) shows decreasing income elasticities of demand as income levels
rise, 2 supporting our hypothesis that the generally higher income level of second homeowners
partly explains their lower overall elasticities of total housing demand relative to those not
owning a second home. However, the very low elasticity levels of second homeowners go
beyond what would be expected based on incomes alone. This final test provides compelling
evidence that the choice to adjust consumption by adding a second home rather than by
increasing the value of the primary residence (through trading up to a higher valued home or
making improvements to an existing home) must lower demand elasticities for primary homes
among second homeowners even more.
Exhibit 6 summarizes our income elasticity models. It is worth noting that statistical
significance tests revealed that for the non-elderly sample, the difference in coefficients of
income elasticity of housing demand between those having and not having vacation homes was
significant at the 90 percent confidence level, both in models with and without the wealth
variable. For the elderly sample in neither case is the difference in elasticities significant.
Conclusion
The propensity models reported here are perhaps the first efforts to model the
determinants of second home ownership. We find that especially the age of the household head
but also the minority status of the household head and household income (both current and
2
The bottom income quartile is an exception perhaps because they have a higher utility for basic necessities other
than housing.
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
19
permanent), as well as household non-housing wealth are good predictors of second-home
ownership.
Our income elasticity models produce results consistent with the hypothesis that those
having second homes have somewhat lower income elasticity of housing demand, as their
resources have to be divided among more than one home. Even when including second home
value in measuring housing consumption, homeowners with second homes still have lower
income elasticity.
20
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Exhibit 1: Descriptive Statistics (AHS Data)
Sample Group:
Variables
Less than High School
High School
Some College
College Plus
Minority Status
Under 35
35-44
45-54
55-64
65+
Married Couple without Kids
Married Couple with Kids
Single Parent
Other family Household
Single Person Household
Other Non-Family Household
New England City
New England Suburb
New England Non-metro
Midwest City
Midwest Suburb
Midwest Non-metro
South City
South Suburb
South Non-metro
West City
West Suburb
West Non-metro
Total Value of All Homes
Value of Primary Home
Current Household Income
Having Investment Savings of More
than 20K
Having Recreational 2nd Homes
All Homeowners
Unweighted N
Yes
%
No
5,140 17.5 24,244
9,146 31.1 20,238
7,333 25.0 22,051
7,765 26.4 21,619
4,767 16.2 24,617
4,059 13.8 25,325
6,768 23.0 22,616
6,189 21.1 23,195
4,494 15.3 24,890
7,874 26.8 21,510
10,759 36.6 18,625
8,212 27.9 21,172
1,537 5.2 27,847
2,415 8.2 26,969
5,550 18.9 23,834
911 3.1 28,473
2,961 10.1 26,423
1,617 5.5 27,767
1,990 6.8 27,394
4,057 13.8 25,327
2,464 8.4 26,920
2,069 7.0 27,315
3,520 12.0 25,864
3,729 12.7 25,655
1,819 6.2 27,565
2,735 9.3 26,649
1,151 3.9 28,233
1,256 4.3 28,128
1,256
972
4.3
3.3
%
Mean
SD
82.5
68.9
75.0
73.6
83.8
86.2
77.0
78.9
84.7
73.2
63.4
72.1
94.8
91.8
81.1
96.9
89.9
94.5
93.2
86.2
91.6
93.0
88.0
87.3
93.8
90.7
96.1
95.7
117,520 90,148
115,092 84,158
48,741 38,091
28,128 95.7
28,412 96.7
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
21
Exhibit 2: Descriptive Statistics (SCF Data)
Sample Group: All Homeowners
Variables
Unweighted N
Yes
%
No
Less than High
1,418 8.6 14,977
School Education
High School
Education
3,349 20.4 13,046
Some College
2,870 17.5 13,525
College Graduate and
Higher
8,758 53.4 7,637
Minority Status
2,397 14.6 13,998
Age Under 35
1,401 8.5 14,994
Age 35-44
2,905 17.7 13,490
Age 45-54
4,250 25.9 12,145
Age 55-64
3,983 24.3 12,412
Age 65+
3,856 23.5 12,539
Married Couples
11,755 71.7 4,640
Male-headed
Households
2,265 13.8 14,130
Female-headed
Households
2,375 14.5 14,020
Total Value of All
Homes
Value of Primary
Home
Current Household
Income
Household Nonhousing Wealth
Have Vacation Home
2,323 14.2 14,072
22
%
Mean
SD
Weighted N
Yes
No
Mean
91.4
10,084,611 13.0 67,329,712 87.0
79.6
82.5
21,595,072 27.9 55,819,252 72.1
17,012,350 22.0 60,401,974 78.0
46.6
85.4
91.5
82.3
74.1
75.7
76.5
28.3
28,722,291
14,894,182
10,341,166
15,783,863
17,988,831
13,517,649
19,782,815
47,580,287
86.2
12,963,143 16.7 64,451,181 83.3
85.5
16,870,894 21.8 60,543,429 78.2
37.1
19.2
13.4
20.4
23.2
17.5
25.6
61.5
48,692,033
62,520,141
67,073,158
61,630,461
59,425,493
63,896,675
57,631,508
29,834,037
62.9
80.8
86.6
79.6
76.8
82.5
74.4
38.5
1,187,458
3,112,890
263,594 456,240
870,106
1,882,222
246,807 359,768
1,061,331
4,499,026
87,069 250,929
12,259,998 46,399,527
85.8
SD
462,304
2,885,714
3.7 74,528,610 96.3
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Exhibit 3a: Propensity Model for Vacation Home Ownership (AHS Data)
Dependent variable: Owning a Recreational Home
Sample group: All homeowners
Variable
Intercept
Permanent Income (in $10,000s)
Having Savings & Investments Over $20K
Minority
Age 35-44
Age 45-54
Age 55-64
Age 65+ (Elderly)
Married with Children
Single Parents
Other Family type
Single Person
Other Non-family type
New England Suburb
New England Non-metro
Midwest City
Midwest Suburb
Midwest Non-metro
South City
South Suburb
South Non-metro
West City
West Suburb
West Non-metro
Permanent Income(in $10,000s)*Elderly
Coefficients
-5.7521
0.2671
0.3951
-0.3973
0.8688
1.3011
1.8718
1.0153
-0.1936
-0.3904
-0.8844
-0.0958
-0.3631
-0.1537
0.0987
-0.0982
-0.0414
-0.1117
-0.0297
-0.1107
-0.2279
-0.1410
-0.0602
-0.2206
0.2660
Odds ratio
***
**
**
***
***
***
***
~
ns
***
ns
ns
ns
ns
ns
ns
ns
ns
ns
ns
ns
ns
ns
***
1.306
1.484
0.672
2.384
3.673
6.5
2.76
0.824
0.677
0.413
0.909
0.696
0.857
1.104
0.906
0.959
0.894
0.971
0.895
0.796
0.869
0.942
0.802
1.305
Note: ~ p <.10
* p <.05
** p <.01
*** p <.001
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
23
Exhibit 3b: Propensity Model for Vacation Home Ownership (SCF Data)
Dependent variable: Owning a Vacation Home
Sample group: All homeowners
Variable
Intercept
Household Income (in $10,000s)
Non Housing Wealth (in $10,000s)
High School Education
Some College
College Graduate and Higher
Minority Status
Age 35-44
Age 45-54
Age 55-64
Age 65+ (Elderly)
Male-headed Households
Female-headed Households
Household Income(in $10,000s)* Elderly
Coefficients
-6.0876
0.0050
0.0009
0.3881
1.1650
1.4906
-0.9540
1.3422
2.2785
2.4220
2.1596
-0.5896
-1.5790
0.0030
Odds ratio
*
***
ns
~
*
*
~
**
**
**
~
***
ns
1.005
1.001
1.474
3.206
4.44
0.385
3.827
9.762
11.268
8.667
0.555
0.206
1.003
Note: ~ p<.10
* p <.05
** p <.01
*** p <.001
24
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Exhibit 4a: Elasticity Model using Predicted Permanent Income & Wealth Variables
(Non-Elderly)
Sample group: Non-Elderly Homeowners
Dependent variable:
Sample Sub-Group:
Intercept
Predicted permanent
income (in $10,000s)
Having Savings &
Investments Over $20K
Minority
Age 35-44
Age 45-54
Age 55-64
Married with kids
Single parents
Other family type
Single person
Other non-family type
New England Suburb
New England Nonmetro
Midwest City
Midwest Suburb
Model 1
Value of primary
home
Do not own a
vacation home
-1.6110
Model 2
Value of primary
home
Own a vacation
home
0.9363
Model 3
Total value of all
homes
Own a vacation
home
3.1226
Model 4
Value of vacation
home(s)
Own a vacation
home
3.1082
Model 5
Value of all
homes
All non-elderly
homeowners
1.1814
***
0.9741
***
0.8343
***
0.7237
**
1.5382
1.1750
0.0341
ns
-0.2720
~
-0.3273
*
-0.3932
ns
0.0206
ns
0.0213
0.0147
0.0452
0.2843
0.0719
0.3478
0.0539
0.3302
-0.0337
ns
ns
**
***
***
***
*
***
ns
0.1925
-0.1388
-0.1167
0.1052
0.1220
0.3153
-0.0223
0.2166
-0.0802
~
ns
ns
ns
ns
ns
ns
ns
ns
0.0784
-0.1127
-0.0914
0.0091
0.0567
0.2272
0.1098
0.3546
-0.0525
ns
ns
ns
ns
ns
ns
ns
**
ns
0.0489
-0.1530
-0.1143
-0.1894
-0.0756
0.1944
0.3299
0.5761
0.1189
ns
ns
ns
ns
ns
ns
ns
**
ns
ns
ns
**
***
***
***
*
***
ns
0.2006
0.1056
***
**
0.1257
0.3636
ns
~
0.0116
0.3665
ns
**
0.1789
0.7736
0.0218
0.0145
0.0442
0.2805
0.0724
0.3454
0.0551
0.3317
0.0331
ns 0.1945
** 0.1099
-0.1737
***
0.1363
ns
-0.0355
ns
0.0347
ns
***
0.0029
ns
0.0122
ns
-0.1514
ns
-0.0911
ns
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
0.1732
-
***
***
**
ns
25
Exhibit 4a: Elasticity Model using Predicted Permanent Income & Wealth Variables
(Non-Elderly)
Sample group: Non-Elderly Homeowners
Dependent variable:
Sample Sub-Group:
Midwest Non-metro
South City
South Suburb
South Non-metro
West City
West Suburb
West Non-metro
Own a Vacation Home
R-squared
Model 1
Value of primary
home
Do not own a
vacation home
Model 2
Value of primary
home
Own a vacation
home
Model 3
Total value of all
homes
Own a vacation
home
Model 4
Value of vacation
home(s)
Own a vacation
home
-0.1586
***
-0.0776
ns
-0.2995
*
-0.3196
ns
-0.0479
ns
-0.0986
ns
-0.2755
ns
-0.1047
ns
-0.0263
ns
0.0576
ns
-0.1005
ns
0.0630
ns
-0.2027
***
0.0411
ns
-0.1694
ns
-0.1764
ns
0.3884
0.3738
0.1520
***
***
***
0.3840
0.3752
-0.1161
*
*
ns
0.2318
0.4075
-0.2153
ns
**
ns
0.1494
0.5040
-0.0615
ns
~
ns
0.2354
0.2301
0.2630
.1287
Model 5
Value of all
homes
All non-elderly
homeowners
0.0023
0.1631
0.0532
0.0286
0.2032
0.3843
0.3740
0.1426
0.6946
***
ns
ns
***
***
***
***
***
0.2509
Note: ~ p <.10
* p <.05
** p <.01
*** p <.001
26
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Exhibit 4b: Elasticity Model using Predicted Permanent Income & Wealth Variables
(Elderly)
Sample Group: Elderly Homeowners
Model 1
Model 2
Model 3
Dependent Variable:
Value of primary
home
Value of primary
home
Total value of all
homes
Model 4
Value of
vacation
home(s)
Sample Sub-group:
Do not own a
vacation home
Own a vacation
home
Own a vacation
home
Own a vacation
home
Intercept
Predicted permanent
income (in $10,000s)
Savings &
Investments Over
$20K
Minority
Married with kids
Single parents
Other family type
Single person
Other non-family
type
New England Suburb
New England Nonmetro
Midwest City
Midwest Suburb
4.3833
0.6643
***
6.2127
0.5208
**
6.8609
0.5230
**
5.8369
0.5408
0.0749
**
-0.3180
*
-0.3630
*
-0.0451
0.0458
-0.2238
ns
ns
ns
-0.2572
1.3486
0.0000
ns
*
NA
-0.1809
1.5085
0.0000
0.0317
0.2980
-0.0305
ns
***
ns
0.3511
0.2246
-0.1464
ns
ns
ns
0.2538
0.0584
***
ns
0.1125
-0.1768
-0.1281
0.0023
**
ns
-0.2419
-0.2337
Model 5
Value of all homes
All elderly
homeowners
~
4.4123
0.6618
***
-0.5054
~
0.0680
**
ns
*
NA
-0.2659
1.9337
0.0000
-0.0484
0.0798
-0.2267
ns
ns
ns
0.2368
0.4152
-0.1108
ns
*
ns
-0.0058
0.8192
0.2406
ns
~
N
A
ns
*
ns
0.0326
0.2976
-0.0306
ns
***
ns
ns
ns
-0.1024
-0.1438
ns
ns
-0.5305
-0.1841
ns
ns
0.2471
-0.1438
***
ns
ns
ns
-0.4009
-0.4886
ns
~
-0.6424
-0.9928
ns
~
-0.1297
-0.0053
**
ns
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
27
Exhibit 4b: Elasticity Model using Predicted Permanent Income & Wealth Variables
(Elderly)
Sample Group: Elderly Homeowners
Dependent Variable:
Sample Sub-group:
Midwest Non-metro
South City
South Suburb
South Non-metro
West City
West Suburb
West Non-metro
Own a Vacation
Home
R-squared
Model 1
Model 2
Model 3
Value of primary
home
Value of primary
home
Total value of all
homes
Model 4
Value of
vacation
home(s)
Do not own a
vacation home
-0.0938
~
0.02576
ns
-0.08877
~
-0.15649
**
0.45768 ***
0.33943 ***
0.20072 ***
Own a vacation
home
-0.4499
ns
-0.11892
ns
0.04567
ns
0.03585
ns
0.2668
ns
0.29476
ns
0.19681
ns
Own a vacation
home
-0.7384
*
-0.28319
ns
0.04439
ns
-0.39357
ns
-0.01365
ns
-0.01042
ns
-0.07404
ns
Own a vacation
home
-1.1928
*
-0.58427 ns
0.01921 ns
-1.79853 **
-0.42189 ns
-0.68952 ns
-0.68283 ns
0.2798
0.2650
0.2066
0.1799
Model 5
Value of all homes
All elderly
homeowners
-0.1013
**
0.024
ns
-0.0835
**
-0.15873 ***
0.45
***
0.33476
***
0.19816
***
0.67716
***
0.1990
Note: ~ p <.10
* p <.05
** p <.01
*** p <.001
28
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Exhibit 4c: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable
(same as Model 4a but without “Savings & Investments over $20K”)
Sample group: Non-Elderly Homeowners
Model 1
Model 2
Model 3
Dependent variable:
Value of primary
home
Value of primary
home
Total value of all
homes
Sample Sub-Group:
Do not own a
vacation home
Own a vacation
home
Own a vacation
home
Intercept
Predicted permanent
income (in $10,000s)
Minority
Age 35-44
Age 45-54
Age 55-64
Married with kids
Single parents
Other family type
Single person
Other non-family type
New England Suburb
New England Nonmetro
Midwest City
Midwest Suburb
Midwest Non-metro
South City
South Suburb
-1.6109
1.1814
***
0.7233
0.9941
***
3.0282
0.8438
0.0208
0.0148
0.0456
0.2858
0.0720
0.3481
0.0539
0.3312
-0.0330
0.2004
0.1057
ns
ns
**
***
***
***
*
***
ns
***
**
0.1923
-0.1417
-0.1288
0.1039
0.1252
0.3067
-0.0068
0.2157
-0.0968
0.1221
0.3322
~
ns
ns
ns
ns
ns
ns
ns
ns
ns
~
-0.1738
0.0028
-0.1584
-0.0478
-0.0263
***
ns
***
ns
ns
0.1166
0.0066
-0.0901
-0.1098
0.0509
ns
ns
ns
ns
ns
Model 4
Value of
vacation
home(s)
Own a vacation
home
***
2.8045
0.7523
0.0766
-0.1231
-0.1017
0.0074
0.0572
0.2129
0.1261
0.3468
-0.0763
0.0094
0.3285
ns
ns
ns
ns
ns
ns
ns
**
ns
ns
~
-0.0582
-0.1737
-0.3158
-0.2915
-0.1092
ns
ns
~
~
ns
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may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Model 5
Value of all
homes
All non-elderly
homeowners
**
-1.5378
1.1749
***
0.0485
-0.1574
-0.1317
-0.1912
-0.0711
0.1818
0.3523
0.5745
0.0948
0.1738
0.7283
ns
ns
ns
ns
ns
ns
ns
**
ns
ns
*
0.0215
0.0146
0.0444
0.2814
0.0724
0.3456
0.0550
0.3323
-0.0327
0.1944
0.1100
ns
ns
**
***
***
***
*
***
ns
***
**
0.0063
-0.0995
-0.3378
-0.1209
0.0534
ns
ns
ns
ns
ns
-0.1732
-0.0023
-0.1630
-0.0531
-0.0286
***
ns
***
ns
ns
29
Exhibit 4c: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable
(same as Model 4a but without “Savings & Investments over $20K”)
Sample group: Non-Elderly Homeowners
Model 1
Model 2
Model 3
Dependent variable:
Value of primary
home
Value of primary
home
Total value of all
homes
Sample Sub-Group:
Do not own a
vacation home
Own a vacation
home
Own a vacation
home
South Non-metro
West City
West Suburb
West Non-metro
Own a Vacation Home
R-squared
-0.2026
0.3886
0.3739
0.1527
0.2354
***
***
***
***
0.0377
0.3682
0.3671
-0.1769
0.2250
ns
~
*
ns
-0.1757
0.2135
0.3993
-0.2893
0.2508
ns
ns
*
ns
Model 4
Value of
vacation
home(s)
Own a vacation
home
-0.1814
0.1266
0.4923
-0.1494
.1238
ns
ns
~
ns
Model 5
Value of all
homes
All non-elderly
homeowners
-0.2032
0.3845
0.3741
0.1431
0.6949
***
***
***
***
***
0.2509
Note: ~ p <.10
* p <.05
** p <.01
*** p <.001
30
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Exhibit 4d: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable
(same as Model 4b but without “Savings & Investments over $20K”)
Sample Group: Elderly Homeowners
Model 1
Model 2
Model 3
Dependent Variable:
Value of primary
home
Value of primary
home
Total value of all
homes
Model 4
Value of
vacation
home(s)
Sample Sub-group:
Do not own a
vacation home
Own a vacation
home
Own a vacation
home
Own a vacation
home
Intercept
Predicted permanent
income (in $10,000s)
Minority
Married with kids
Single parents
Other family type
Single person
Other non-family
type
New England Suburb
New England Nonmetro
Midwest City
Midwest Suburb
Midwest Non-metro
South City
South Suburb
4.3661
0.6663
***
5.8300
0.5519
**
6.4240
0.5586
**
5.2286
0.5904
-0.0490
0.0400
-0.2265
ns
ns
ns
-0.1962
1.3571
0.0000
ns
*
NA
-0.1112
1.5182
0.0000
ns
*
NA
-0.1688
1.9472
0.0000
0.0299
0.3037
-0.0262
ns
***
ns
0.3317
0.1535
-0.1344
ns
ns
ns
0.2146
0.3340
-0.0970
ns
~
ns
0.2577
0.0623
***
ns
0.1136
-0.1441
ns
ns
-0.1011
-0.1065
-0.1228
0.0066
-0.0852
0.02862
-0.08564
*
ns
ns
ns
~
-0.2140
-0.1814
-0.3940
-0.05629
0.06143
ns
ns
ns
ns
ns
-0.3691
-0.4290
-0.6746
-0.21169
0.06238
Model 5
Value of all homes
~
All elderly
homeowners
4.3983
0.6635
***
-0.0521
0.0744
-0.2292
~
ns
ns
-0.0367
0.7062
0.2597
ns
~
N
A
ns
*
ns
0.1597
0.3029
-0.0267
ns
***
ns
ns
ns
-0.5286
-0.1321
ns
ns
0.2507
0.0606
***
ns
ns
ns
*
ns
ns
-0.5981
-0.9098
-1.1039
-0.48473
0.04425
ns
ns
~
ns
ns
-0.1249
-0.0017
-0.0938
0.02645
-0.08075
*
ns
~
ns
~
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
31
Exhibit 4d: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable
(same as Model 4b but without “Savings & Investments over $20K”)
Sample Group: Elderly Homeowners
Model 1
Model 2
Model 3
Dependent Variable:
Value of primary
home
Value of primary
home
Total value of all
homes
Model 4
Value of
vacation
home(s)
Sample Sub-group:
Do not own a
vacation home
Own a vacation
home
Own a vacation
home
Own a vacation
home
South Non-metro
West City
West Suburb
West Non-metro
Own a Vacation
Home
R-squared
-0.15423
0.46045
0.34438
0.20717
0.1791
**
***
***
***
0.10301
0.29434
0.30352
0.25103
0.2583
ns
ns
ns
ns
-0.3169
0.01778
-0.000414
-0.01215
0.2373
ns
ns
ns
ns
-1.69179
-0.37813
-0.67559
-0.59667
0.1901
Model 5
Value of all homes
**
ns
ns
ns
All elderly
homeowners
-0.15685
0.45241
0.3393
0.2037
0.67769
**
***
***
***
***
0.1984
Note: ~ p <.10
* p <.05
** p <.01
*** p <.001
32
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Exhibit 5: Demand elasticities decline with income among higher-income non-elderly
homeowners, except for low-income households who have strived a lot to achieve
homeownership
Do not own a second home
Annual Permanent
Income
Household Income
Quartile
Level
High
Over $61,578
HighMid
$49,840 - $61,578
LowMid
$40,140 - $49,839
Low
Less than $40,140
Overall
Mean
$50,934
Income Elasticity of
Primary Housing
Demand
1.00
1.28
1.66
0.92
1.18
Own a Second Home
Annual Permanent
Income Elasticity of
Household Income
Primary Housing
Income Elasticity of Total
Level
Demand
Housing Demand
Overall
$56,568
0.97
0.83
Mean
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may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
33
Exhibit 6: Summary Table of Income Elasticity of Housing Demand
Sample Group: Non-Elderly Homeowners
Dependent variable
Sample Sub-groups
Value of primary home
Value of primary home
Value of all homes
Do not own a vacation home
Own a vacation home
Own a vacation home
Income Elasticity
With Wealth
Without Wealth
Control
Control
Variable
1.18137 ***
1.18136 ***
0.97407 ***
0.99413 ***
0.83426 ***
0.84375 ***
Sample Group: Elderly Homeowners
Dependent variable
Sample Sub-groups
Value of primary home
Value of primary home
Value of all homes
Do not own a vacation home
Own a vacation home
Own a vacation home
Income Elasticity
With Wealth
Without Wealth
Control
Control
Variable
0.66429 ***
0.66632 ***
0.52075 **
0.55193 **
0.52298 **
0.55856 **
Note: ~ p <.10
* p <.05
** p <.01
*** p <.001
34
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may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
References
Belsky, Eric and Prakken, Joel. 2004. Housing Wealth Effects: Housing Impact on Wealth
Accumulation, Wealth Distribution, and Consumer Spending. National Association of Realtors®
National Center for Real Estate Research.
Carliner, Geoffery. 1973. Income Elasticity of Housing Demand. The Review of Economics and
Statistics.
Carliner, Michael. 1990. Second Home. Housing Economics, July Issue.
Carliner, Michael. 1998. Second Home Construction. Housing Economics, July Issue.
Carliner, Michael. 2002. Second Homes: A Growing Market? Housing Economics, July Issue.
DeLeeuw, F. 1971. The Demand for Housing. Review of Economics and Statistics, February
Issue.
Di, Zhu Xiao; McArdle, Nancy; Masnick, George S. 2001. Second Homes: What, How Many,
Where and Who. Joint Center for Housing Studies, Harvard University. Working Paper series
N01-2.
Fallis, G. 1985. The Demand For Housing. Housing Economics. Toronto: Butterworths.
Goodman, Allen C. and Kawai, Masahiro. 1982. Permanent Income, Hedonic Prices, and
Housing Demand: New Evidence. Journal of Urban Economics. Vol 12.
Goodman, Allen C. and Kawai, Masahiro. 1984. Replicative Evidence on the Demand for
Owner-Occupied and Rental Housing. Southern Economic Journal.
Goodman, Allen C. 1990. Demographics of Individual Housing Demand. Regional Science and
Urban Economics. Vol 20. pp. 83-102.
Gutierrez, Rose. 1999. Second Homes: Well Hidden. Housing Economics, October Issue.
Hansen J.L.; Formby J.P.; Smith W.J. 1998. Estimating the Income Elasticity of Demand for
Housing: A Comparison of Traditional and Lorenz-Concentration Curve Methodologies. Journal
of Housing Economics.
Kochera, Andrew. 1997. “Second” Homes Owners by Households. Housing Economics,
November Issue.
Kohlhase, Janet E. 1986. Labor Supply and Housing Demand for One-and Two-Earner
Households. The Review of Economics and Statistics.
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
35
Muth, R. F. 1965. The Stock Demand Elasticities for Non-Farm Housing. The Review. 47,
November Issue.
National Association of Home Builders. 2000. What 21st Century Home Buyers Want.
Polinsky, A. Mitchell, and Ellwood, David T. 1979. An Empirical Reconciliation of Micro and
Grouped Estimates of the Demand for Housing. The Review of Economics and Statistics.
Reid, M. 1962. Housing and Income. Chicago: University of Chicago Press.
United States Department of Housing and Urban Development, 2004. How Many Second
Homes Are There? Housing Market Conditions.
Wachter, Susan M. and Megbolugbe, Isaac F. 1992. Racial and Ethnic Disparities in
Homeownership. Housing Policy Debate. 3(2)
Winger, A. 1968. Housing and Income. Western Economic Journal. 6. June Issue
36
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may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Appendix Table 1:
Permanent Income Regression (Box-Cox λ=0.5)
Variable
DF Coefficient
Intercept
High School
Some College
College Graduate or
Higher
Minority
Age 35-44
Age 45-54
Age 55-64
Age 65+
Married with children
Single parents
Other family type
Single Person Household
Other non-family type
New England Suburb
New England Non-metro
Midwest City
Midwest Suburb
Midwest Non-metro
South City
South Suburb
South Non-metro
West City
West Suburb
West Non-metro
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Root MSE
Adjusted R. Square
N
Mean
Square
1.109E8
3725311
1.11E7
4.126E7
F Value
Pr > F
403.86801
35.38528
65.19025
127.61739
Type II Sum
of Squares
1.109E8
3725311
1.11E7
4.126E7
6785.57
227.91
679.24
2524.14
<.0001
<.0001
<.0001
<.0001
-24.84862
24.90867
33.39170
-7.97708
-81.02657
-4.44193
-100.95346
-41.75909
-116.24828
-38.83794
21.33853
-18.22930
-8.13391
4.77603
-25.81154
-17.94502
-12.29114
-36.61865
5.97286
5.68575
-24.32725
2040145
1501197
2498400
109798
1.294E7
60606
1.148E7
3199519
4.584E7
1178943
379576
222799
49158
20730
523873
241412
134174
1198814
24587
26090
334514
2040145
1501197
2498400
109798
1.294E7
60606
1.148E7
3199519
4.584E7
1178943
379576
222799
49158
20730
523873
241412
134174
1198814
24587
26090
334514
124.81
91.84
152.85
6.72
791.76
3.71
702.51
195.74
2804.29
72.13
23.22
13.63
3.01
1.27
32.05
14.77
8.21
73.34
1.50
1.60
20.46
<.0001
<.0001
<.0001
0.0096
<.0001
0.0542
<.0001
<.0001
<.0001
<.0001
<.0001
0.0002
0.0829
0.2601
<.0001
<.0001
0.0042
<.0001
0.2200
0.2065
<.0001
127.85071
0.3523
27908
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
37
Appendix Table 2:
38
Variable Definitions for Permanent Income Regression
Variable
Definition
High School
Some College
College Graduate or Higher
Minority
Age 35-44
Age 45-54
Age 55-64
Age 65+
Married with children
Single parents
Other family type
Single Person Household
Other non-family type
New England Suburb
New England Non-metro
Midwest City
Midwest Suburb
Midwest Non-metro
South City
South Suburb
South Non-metro
West City
West Suburb
West Non-metro
1 if high school graduate, 0 otherwise
1 if some college education, 0 otherwise
1 if college graduate, 0 otherwise
1 if minority, 0 otherwise
1 if 35-44, 0 otherwise
1 if 45-54, 0 otherwise
1 if 55-64, 0 otherwise
1 if 65 or over, 0 otherwise
1 if married with kids, 0 otherwise
1 if single parents, 0 otherwise
1 if other family type, 0 otherwise
1 if single person household, 0 otherwise
1 if other non-family type household, 0 otherwise
1 if NE suburb, 0 otherwise
1 if NE non-metro, 0 otherwise
1 if Midwest city, 0 otherwise
1 if Midwest sub, 0 otherwise
1 if Midwest non-metro, 0 otherwise
1 if South city, 0 otherwise
1 if South sub, 0 otherwise
1 if South non-metro, 0 otherwise
1 if West city, 0 otherwise
1 if West sub, 0 otherwise
1 if West non-metro, 0 otherwise
© 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to the source.